CN103761703A - Single channel color image encryption method based on GT conversion and chaos - Google Patents

Abstract

A single channel color image encryption method based on GT conversion and chaos relates to two encryption frames. In the first encryption frame, first, normalization operation is performed on a color image, and the normalized image is decomposed into three red, green and blue component images; then, Arnold conversion is performed on the three component images to perform pixel permutation; finally, Logistic chaotic mapping, tent chaotic mapping and Gyrator conversion with an rotating angle of alpha are used for combining the three component images in chaos into data information relevant to a three-channel structure; in the second encryption frame, first, Arnold conversion is performed on data information relevant to the three-channel structure; then, phase modulation is performed on the Arnold conversion result; finally, Gyrator conversion is performed on a phase modulation result, the encryption process is completed, and gray image information is obtained.

Description

Single channel color image encrypting method based on GT conversion and chaos

Technical field

The invention belongs to virtual optics information ciphering method technical field, relate to a kind of based on GT(revolution) the single channel color image encrypting method of conversion and chaos.

Background technology

In recent years, optical encryption technology is being played the part of more and more important effect in information security.Since Refregier and Javidi propose to encrypt based on double random phase, researcher proposes various image encryption technology, for example, and the fractional fourier transform of fractional fourier transform and expansion, phase place rejuvenation and the operation of random pixel scramble.The major defect of these methods is to use single beam to irradiate input picture, and the chromatic information of deciphering image is lost.Therefore color image encryption has become a severe problem, becomes a difficult problem for optical application.

Karim etc. propose the color image encrypting method based on thumbnail and two random mask.Zhao Daomu etc. are used wavelength-division multiplex and encrypt coloured image without lens Fresnel transform hologram, also have scholar to propose the image encryption algorithm that conversion is used two step phase shift interferences and Arnold to convert based on gyrator.Zhao Daomu and Chen Linfeng have not only proposed based on wavelength-division multiplex with without the multicolor image encryption algorithm of lens Fresnel transform hologram, and the chromatic information also having proposed based on fractional fourier transform and digital hologram is encrypted and composition algorithm.Joshi etc. propose the non-linear color image encryption scheme based on fractional fourier transform and natural logarithm.Chen Wen etc. propose the multicolor image encryption algorithm based on Arnold conversion and interference technique.Liu Zhengjun etc. propose the color image encrypting method of discrete cosine transform domain based on Arnold conversion and blend of colors operation, and the location of pixels of three passages of Arnold conversion scramble coloured image for the method, changes pixel value with discrete cosine transform.Muhammad not only proposes in GT territory, based on discrete cosine transform and the chromatic information encryption method of Hilbert phase bitmask radially, also to propose the chromatic information encryption method based on Arnold conversion.Hwang proposes the image encryption algorithm of Fresnel transform territory based on improving Gerchberg – Saxton algorithm.

Yet above-mentioned algorithm all belongs to hyperchannel to be encrypted, three passages of RGB that are about to coloured image are encrypted separately, are deciphered, and can make like this complexity of these encryption systems improve.In order to overcome this problem, researcher has proposed the various color image encryption schemes based on single channel technology.In the encipherment scheme that Liu Hongjun and Wang Xingyuan propose, first the coloured image of M * N pixel is converted to the gray level image of M * 3N, then use the sequence that segmentation chaotic maps produces to implement the horizontal scramble in position to this gray level image, next the picture breakdown after scramble is become to three parts, to this three part, use respectively Chen system to realize and obscure, spread.

Chen Wen proposes the optical asymmetric encryption system of the thumbnail based on coloured image, has used the phase truncation strategy in Fresnel territory in this system.Zhou Nanrun etc. have proposed the color image encryption scheme based on chaotic maps and fractional fourier transform, and in this scheme, form and aspect saturation magnetization is first encrypted or be decrypted into coloured image.In addition, Zhou Nanrun etc. have proposed the non-linear multicolor image encryption algorithm of mark Mellin transform based on real-time storage, and in this algorithm, ciphertext is real-time, are easy to show, transmit, store.Deng Xiaopeng has proposed a single channel asymmetric encipherment system with Zhao Daomu one width color image encryption has been become to a real-valued gray scale ciphertext, makes like this decrypting process quite simple.Above-mentioned algorithm is all the color image encryption based on single channel technology, although they have simplified ciphering process to a certain extent, still has the problems such as key space is little, security is low.

Summary of the invention

The object of the invention is to propose a kind of single channel color image encrypting method based on GT conversion and chaos, solve the problem that key space is little, security is low that prior art exists.

The technical solution adopted in the present invention is that the single channel color image encrypting method based on GT conversion and chaos, comprises two infill layer frameworks; Ground floor is encrypted in framework, first, coloured image is implemented normalization operation and be red (R), green (G) and blueness (B) three component images by the picture breakdown after normalization; Then, three component images are implemented respectively to Arnold conversion and carry out pixel scramble; Finally, use the Gyrator conversion that Logistic chaotic maps, tent chaotic maps, the anglec of rotation are α, three component images after scramble are combined as to the data message that triple channel structure is relevant; At the second layer, encrypt in framework, first, the relevant data message of this triple channel structure is carried out to Arnold conversion; Then, the result of Arnold conversion is implemented to phase-modulation; Finally, the result of phase-modulation is implemented to Gyrator conversion, complete whole encryption flow, obtain final gray level image information.

Feature of the present invention is also:

Ground floor is encrypted framework and is specifically comprised:

The first step: original color image is carried out to normalization operation, and be decomposed into R, G, tri-component images of B, be expressed as r (x, y), g (x, y) and b (x, y), in every width component image, pixel maximal value is 1;

Second step: it is n that component image r (x, y), g (x, y) and b (x, y) are implemented respectively to iterations ₃, n ₂and n ₁arnold conversion, the noise image after scramble is expressed as A _n3(r (x, y)), A _n2(g (x, y)) and A _n1(b (x, y));

The 3rd step: first obtain first CHAOTIC PHASE MODULATED function, the blue component A of this function after by scramble _n1(b (x, y)) and Logistic Chaotic map sequence C ₁(x, y) combines, and is exp{i π (A _n1(b (x, y))+C ₁(x, y)) }; By the green component A after scramble _n2(g (x, y)) is complex signal H with first CHAOTIC PHASE MODULATED combination of function ₁(x, y), to H ₁(x, y) implements the Gyrator that the anglec of rotation is α and converts the intermediate variable H that obtains green component and blue component _gb(x, y), H _gbthe amplitude of (x, y) is T _gb(x, y), phase place is angle{H _gb(x, y) }; Then calculate second CHAOTIC PHASE MODULATED function, this function is by angle{H _gb(x, y) } and two-dimentional asymmetric tent sequence of mapping C ₂(x, y) forms, and is exp{i π (angle{H _gb(x, y) }+C ₂(x, y)) }; By the red component A after scramble _n3(r (x, y)) is complex signal H with second CHAOTIC PHASE MODULATED combination of function ₂(x, y), to H ₂(x, y) carries out the Gyrator conversion that the anglec of rotation is α, generates the relevant data message H of triple channel _rgb(x, y).

The second layer is encrypted framework and is specially: the first data message H relevant to triple channel _rgb(x, y) implements iterations is n ₄arnold conversion, result and the chaos sequence exp{i π (C of modulation Arnold conversion ₁(x, y)+C ₂(x, y) }, to exchange the result making and implement α rank Gyrator conversion, the amplitude that extracts transformation results obtains final ciphertext I _final, the phase place of extracting transformation results obtains final phase place P _final.

Above-mentioned ground floor is encrypted in the second step of framework, and Arnold is transformed to:

$A_M:\left[\begin{array}{c}{x}^{\′}\\ y^{\′}\end{array}\right]\mathrm{ARP}[f(x,y),M]=\mathrm{mod}\left(\begin{array}{c}\left[\begin{array}{cc}1& 1\\ 1& 2\end{array}\right]\left[\begin{array}{c}x\\ y\end{array}\right],M\end{array}\right)---\left(1\right)$

Formula (1) has defined Arnold conversion, wherein ART represents Arnold conversion, f (x, y) for treating the plaintext image of scramble, f (x, y) size is M * M, (x, y) and (x ', y ') represent respectively Arnold conversion scramble before and the location of pixels after scramble, mod () accords with for complementation.

Above-mentioned ground floor is encrypted in the 3rd step of framework, and Gyrator is transformed to:

$f_o(x_o,y_o)=G^{\mathrm{\α}}\left[f_i(x_i,y_i)\right](x_o,y_o)=\frac{1}{\left|\sin \mathrm{\α}\right|}\∫\∫f_i(x_i,y_i)K_{\mathrm{\α}}(x_i,y_i,x_o,y_o){\mathrm{dx}}_i{\mathrm{dy}}_i---\left(2\right)$

Formula (2) has defined optical imagery f _i(x _i, y _i) the result f of α level Gyrator conversion _o(x _o, y _o), K wherein _α(x _i, y _i, x _o, y _o) be the integral kernel function of Gyrator conversion, α is the progression (being the anglec of rotation) of Gyrator conversion, G ^αrepresent α level Gyrator conversion, (x _i, y _i) and (x _o, y _o) represent respectively input, output plane coordinate, ∫ ∫ f _i(x _i, y _i) K _α(x _i, y _i, x _o, y _o) dx _idy _iexpression is to function f _i(x _i, y _i) K _α(x _i, y _i, x _o, y _o) respectively at x _idirection and y _idirection is done integral operation.Sin α is the sine value of progression (being the anglec of rotation) α;

$K_{\mathrm{\α}}(x_i,y_i,x_o,y_o)=\exp \left(i2\mathrm{\π}\frac{(x_o{y}_o+x_i{y}_i)\cos \mathrm{\α}-(x_i{y}_o+x_o{y}_i)}{\sin \mathrm{\α}}\right)---\left(3\right)$

Formula (3) has defined the integral kernel function K of Gyrator conversion _α(x _i, y _i, x _o, y _o), wherein, exp () is exponent arithmetic, and i is the imaginary part of symbol, and π is circular constant, and sin α is the sine value of progression (being the anglec of rotation) α.Cos α is the cosine value of progression (being the anglec of rotation) α.X _ifor input plane x direction coordinate, y _ifor input plane y direction coordinate, x _ofor output plane x direction coordinate, y _ofor output plane y direction coordinate.Hence one can see that, when α=0, and G ⁰{ f _i(x _i, y _i)=f _i(x _i, y _i); It when α=pi/2, is the Fourier transform of coordinate axis rotation pi/2; It when α=π, is inverse Fourier transform; When the pi/2 of α=3, be the inverse Fourier transform of coordinate axis rotation pi/2, when α is other order, the integral kernel K of Gyrator conversion _α(x _i, y _i, x _o, y _o) there is continuous amplitude and hyperbolic curve phase structure.

Above-mentioned ground floor is encrypted in the 3rd step of framework, and Logistic is mapped as:

f(x)＝p·x·(1-x) （4）

Formula (4) has defined 1 dimensional Logistic Map, and wherein fractal parameter p is constant, and 0 < p≤4, and x is independent variable, and f (x) is Logistic mapping value.

x _n+1＝p·x _n·(1-x _n) （5）

Formula (5) is the iteration form of formula (4), and wherein, fractal parameter p is constant, and 0 < p≤4, x _n, x _n+1for chaos sequence value, and x _n∈ (0,1), x _n+1∈ (0,1).

Above-mentioned ground floor is encrypted in the 3rd step of framework, and tent is mapped as:

$x_{n+1}=\left\{\begin{array}{c}\frac{x_n}{q}(0\&le;x_n\&le;q)\\ \frac{1-x_n}{1-q}(q\&le;x_n\&le;1)\end{array}\right.---\left(6\right)$

Formula (6) has defined tent mapping, wherein x _n, x _n+1the iteration result that represents the n time and the n+1 time, x ₀for iteration initial value, q is parameter, and when q ∈ (0,1), formula (6) is in chaos state.

Above-mentioned ground floor is encrypted in the 3rd step of framework, complex signal H ₁(x, y) is:

H ₁(x,y)＝A _n2(g(x,y))·exp{iπ(A _n1(b(x,y))+C ₁(x,y))} （7）

Formula (7) has defined the green component A after scramble _n2(g (x, y)) and first CHAOTIC PHASE MODULATED function exp{i π (A _n1(b (x, y))+C ₁(x, y)) } the complex signal H that obtains after combination ₁(x, y).Wherein exp{} is exponent arithmetic, and i is the imaginary part of symbol, and π is circular constant.

Above-mentioned ground floor is encrypted in the 3rd step of framework, complex signal H ₂(x, y) is:

H ₂(x,y)＝A _n3(r(x,y))·exp{iπ(angle{H ₁(x,y)}+C ₂(x,y))} （8）

Formula (8) has defined the red component A after scramble _n3(r (x, y)) and second CHAOTIC PHASE MODULATED function exp{i π (angle{H ₁(x, y) }+C ₂(x, y)) } the complex signal H that obtains after combination ₂(x, y).Wherein exp{} is exponent arithmetic, and i is the imaginary part of symbol, and π is circular constant, and angle{} is for extracting phase operation.

Encryption method of the present invention also comprises decrypting process, and decrypting process is the inverse process of encrypting.Comprise two-layer deciphering framework, ground floor deciphering framework: modulate final ciphertext I _finalwith final phase place P _final, exchange the result enforcement-α rank Gyrator conversion making, the result that modulating transformation obtains and phase place exp{-i π (C ₁(x, y)+C ₂(x, y) }, exchanging the result enforcement iterations making is m ₄contrary Arnold conversion, after conversion, obtain triple channel related data H _rgb(x, y).Second layer deciphering framework is as follows:

The first step: to triple channel related data H _rgb(x, y) enforcement-α rank Gyrator conversion obtains complex signal H ₂(x, y), extracts complex signal H ₂the amplitude of (x, y), it is m that this amplitude is implemented to iterations ₃contrary Arnold conversion obtain red component r (x, y).

Second step: extract complex signal H ₂the phase place of (x, y) obtains angle{H ₂(x, y) }, phase modulation angle{H ₂(x, y) }/π-C ₂(x, y) and amplitude T _gb(x, y), exchanges the result enforcement-α rank Gyrator conversion making and obtains complex signal H ₁(x, y), extracts complex signal H ₁the amplitude of (x, y), it is m that this amplitude is implemented to iterations ₂contrary Arnold conversion obtain green component g (x, y).

The 3rd step: extract complex signal H ₁the phase place of (x, y) obtains angle{H ₁(x, y) }, to phase place angle{H ₁(x, y) }/π-C ₁(x, y) implements iterations is m ₁contrary Arnold conversion obtain blue component b (x, y).Wherein, when plaintext image size is 256 * 256 pixel, m ₁=192-n ₁, m ₂=192-n ₂, m ₃=192-n ₃, m ₄=192-n ₄; When plaintext image size is 512 * 512 pixel, m ₁=384-n ₁, m ₂=384-n ₂, m ₃=384-n ₃, m ₄=384-n ₄.

The present invention has following beneficial effect:

1, use Gyrator transposition encryption coloured image, in its Optical Implementation device, the distance of lens and input, output plane is fixed, and the distance that has overcome lens and input in fractional fourier transform Optical Implementation device, output plane need be according to the shortcoming of different fractional fourier transform angular setting.

2, the present invention combines Gyrator conversion, Arnold conversion, Logistic chaotic maps and tent mapping, uses two-layer encipherment scheme, makes encrypted image have non-linear and randomness, has improved the security of encryption system.

3, the present invention has reduced the complexity of color image encryption system, and system is simple, easy to operate.

Accompanying drawing explanation

Fig. 1 is the encryption method schematic diagram that the present invention is based on the single channel color image encrypting method of GT conversion and chaos.

Fig. 2 is the decryption method schematic diagram that the present invention is based on the single channel color image encrypting method of GT conversion and chaos.

Fig. 3 is that to adopt the ciphertext graph of the original color image " Baboon.jpg " of the single channel color image encrypting method encryption the present invention is based on GT conversion and chaos to look like be gray level image.

Embodiment

Below in conjunction with the drawings and specific embodiments, the present invention is described in detail.

The invention discloses a kind of single channel color image encrypting method based on GT conversion and chaos, the method comprises two infill layer frameworks.

Concrete steps are as follows:

Ground floor is encrypted framework:

The first step: the coloured image " Baboon.jpg " of 512 * 512 pixels of take is example, " Baboon.jpg " carried out to normalization operation, and " Baboon.jpg " after normalization is decomposed into R, G, B component image, be expressed as r (x, y), g (x, y) and b (x, y).

Second step: it is n that component image r (x, y), g (x, y) and b (x, y) are implemented respectively to iterations ₃, n ₂and n ₁arnold conversion, the noise image after scramble is expressed as A _n3(r (x, y)), A _n2(g (x, y)) and A _n1(b (x, y)).

The 3rd step: first obtain first CHAOTIC PHASE MODULATED function, the blue component A of this function after by scramble _n1(b (x, y)) and Logistic Chaotic map sequence C ₁(x, y) combines, i.e. exp{i π (A _n1(b (x, y))+C ₁(x, y)) }.By the green component A after scramble _n2(g (x, y)) is combined as a complex signal H with first chaotic maps modulating function ₁(x, y), to H ₁(x, y) implements the Gyrator conversion that the anglec of rotation is α, is converted into the intermediate variable H of green component and blue component _gb(x, y).H _gbthe amplitude of (x, y) is T _gb(x, y), phase place is angle{H _gb(x, y) }, then obtain second CHAOTIC PHASE MODULATED function, this function is by angle{H _gb(x, y) } and two-dimentional asymmetric tent sequence of mapping C ₂(x, y) forms, i.e. exp{i π (angle{H _gb(x, y) }+C ₂(x, y)) }, by the red component A after scramble _n3(r (x, y)) and second CHAOTIC PHASE MODULATED combination of function are a new complex signal H ₂(x, y), to H ₂(x, y) carries out the Gyrator conversion that the anglec of rotation is α, generates the relevant data message H of triple channel _rgb(x, y).

The second layer is encrypted framework: the first data message H relevant to triple channel _rgb(x, y) implements iterations is n ₄arnold conversion, result and the phase place exp{i π (C of modulation Arnold conversion ₁(x, y)+C ₂(x, y) }, to exchange the result making and implement α rank Gyrator conversion, the phase place of extracting transformation results obtains final phase place P _final, the amplitude that extracts transformation results obtains final ciphertext I _final.

Referring to Fig. 1, the method comprises two infill layer frameworks, and dotted line is ground floor Encryption Model above, and dotted line is second layer Encryption Model below.Ground floor is encrypted in framework, first, original color image is implemented normalization operation and is blue b (x, y), green g (x, y) and three component images of red r (x, y) by the picture breakdown after normalization; It is n that blue b (x, y), green g (x, y) and three components of red r (x, y) are implemented respectively to iterations ₁, n ₂and n ₃arnold conversion carry out pixel scramble, after scramble, obtain respectively A _n1(b (x, y)), A _n2(g (x, y)) and A _n3(r (x, y)); Then, the blue component A after modulating transformation _n1(b (x, y)) and Logistic Chaotic map sequence C ₁(x, y), obtains first CHAOTIC PHASE MODULATED function exp{i π (A _n1(b (x, y))+C ₁(x, y)) }.By the green component A after scramble _n2(g (x, y)) is combined as a complex signal H with first chaotic maps modulating function ₁(x, y), to H ₁(x, y) implements the Gyrator that the anglec of rotation is α and converts the intermediate variable H that obtains green component and blue component _gb(x, y).H _gbthe amplitude of (x, y) is T _gb(x, y), || for extracting amplitude operation, H _gbthe phase place of (x, y) is angle{H _gb(x, y) }, next ask second CHAOTIC PHASE MODULATED function, this function is by angle{H _gb(x, y) } and two-dimentional asymmetric tent sequence of mapping C ₂(x, y) forms, i.e. exp{i π (angle{H _gb(x, y) }+C ₂(x, y)) }.By the red component A after scramble _n3(r (x, y)) and second CHAOTIC PHASE MODULATED combination of function are a new complex signal H ₂(x, y), to H ₂(x, y) implements the Gyrator conversion that the anglec of rotation is α, generates the relevant data message H of triple channel _rgb(x, y).At the second layer, encrypt in framework, first, the data message H relevant to triple channel structure _rgb(x, y) implements iterations is n ₄arnold conversion obtain A _n4(H _rgb(x, y)), the result A of modulation Arnold conversion _n4(H _rgb(x, y)) and phase place exp{i π (C ₁(x, y)+C ₂(x, y) }, exchange the result enforcement α rank Gyrator conversion making and obtain H _final(x, y), extracts H _finalthe phase place of (x, y) obtains final phase place P _final, extract H _finalthe amplitude of (x, y) obtains final ciphertext I _final.Wherein, angle{H _final(x, y) } expression extraction H _finalthe phase place of (x, y), amplitude{H _final(x, y) } expression extraction H _finalthe amplitude of (x, y).G ^αrepresent α rank Gyrator conversion, exp{} represents exponent arithmetic, and i is the imaginary part of symbol, and π is circular constant,

for multiply operation.

Fig. 2 is the decryption method schematic diagram that the present invention is based on the single channel color image encrypting method of GT conversion and chaos, is the inverse process of encryption method.Comprise two-layer deciphering framework, ground floor deciphering framework: modulate final ciphertext I _finalwith final phase place P _final, exchange the result enforcement-α rank Gyrator conversion making, the conjugation exp{-i π (C of the result that modulating transformation obtains and random phase ₁(x, y)+C ₂(x, y) }, exchanging the result enforcement iterations making is m ₄contrary Arnold conversion, after conversion, obtain triple channel related data H _rgb(x, y).Second layer deciphering framework: first, to triple channel related data H _rgb(x, y) enforcement-α rank Gyrator conversion obtains complex signal H ₂(x, y), extracts complex signal H ₂the amplitude of (x, y), it is m that this amplitude is implemented to iterations ₃contrary Arnold conversion obtain red component r (x, y).Secondly, extract complex signal H ₂the phase place of (x, y) obtains angle{H ₂(x, y) }, phase modulation angle{H ₂(x, y) }/π-C ₂(x, y) and amplitude T _gb(x, y), exchanges the result enforcement-α rank Gyrator conversion making and obtains complex signal H ₁(x, y), extracts complex signal H ₂the amplitude of (x, y), it is m that this amplitude is implemented to iterations ₂contrary Arnold conversion obtain green component g (x, y).Finally, extract complex signal H ₁the phase place of (x, y) obtains angle{H ₁(x, y) }, to phase place angle{H ₁(x, y) }/π-C ₁(x, y) implements iterations is m ₁contrary Arnold conversion obtain blue component b (x, y).Wherein, C ₁the chaos sequence that (x, y) produces for Logistic chaotic maps, C ₂the chaos sequence that (x, y) produces for tent mapping, angle{} is phase extraction operation, amplitude{} is amplitude extraction operation.G ^-αexpression-α rank Gyrator conversion, exp{} represents exponent arithmetic, and i is the imaginary part of symbol, and π is circular constant, for multiply operation.

Principle of work of the present invention: the present invention is transformed to master with Gyrator, the Arnold of usining conversion and CHAOTIC PHASE MODULATED are as ancillary technique.The present invention comprises two infill layer frameworks, and ground floor is encrypted in framework, first, coloured image is implemented normalization operation and be red (R), green (G) and blueness (B) three component images by the picture breakdown after normalization; Then, three components are implemented respectively to Arnold conversion and carry out pixel scramble; Finally, use the Gyrator conversion that Logistic chaotic maps, Kent chaotic maps, the anglec of rotation are α, three component images after scramble are combined as to the data message that triple channel structure is relevant.At the second layer, encrypt in framework, first, the relevant data message of this triple channel structure is carried out to Arnold conversion; Secondly, the result of Arnold conversion is implemented to phase-modulation; Finally, the result of phase-modulation is implemented to Gyrator conversion, complete whole encryption flow, obtain final gray level image information.

In the present invention, by the correlativity between neighbor, as the key technical indexes, in order to test the correlativity between neighbor, for original image and ciphertext graph picture, in horizontal, longitudinal and diagonal, 3000 pairs of pixels have been chosen at random respectively.Related coefficient Cor is defined as follows:

$\mathrm{Cor}=\frac{{\mathrm{\&Sigma;}}_{i=1}^N(x_i-\stackrel{\&OverBar;}{x})(y_i-\stackrel{\&OverBar;}{y})}{\sqrt{\left({\mathrm{\&Sigma;}}_{i=1}^N{(x_i-\stackrel{\&OverBar;}{x})}^2\right)\left({\mathrm{\&Sigma;}}_{i=1}^N{(y_i-\stackrel{\&OverBar;}{y})}^2\right)}}---\left(9\right)$

Formula (9) has defined the related coefficient between neighbor, wherein x _iand y _itwo neighbor gray-scale values in image, N=3000, $\stackrel{\&OverBar;}{x}=(1/N){\mathrm{\&Sigma;}}_{i=1}^N{x}_i,\stackrel{\&OverBar;}{y}=(1/N){\mathrm{\&Sigma;}}_{i=1}^N{y}_i.$

Table 1 is the correlativity calculation result of original image, ciphertext graph picture and PHASE DISTRIBUTION image, data from table are known, the degree of correlation in original image between neighbor is higher, the degree of correlation in ciphertext graph picture, PHASE DISTRIBUTION image between neighbor is very little, and therefore general disabled user can not look like to obtain from ciphertext graph any useful information of relevant original image.

The related coefficient of table 1 original image and ciphertext graph picture

Shown in Fig. 3, be to utilize the encrypted result of single channel color image encrypting method to a width coloured image the present invention is based on GT conversion and chaos, ciphertext graph looks like to present white noise and distributes, and therefore general disabled user can not look like to obtain from ciphertext graph any useful information of relevant original image.

Claims (10)

1. the single channel color image encrypting method based on GT conversion and chaos, is characterized in that, comprises two infill layer frameworks; Ground floor is encrypted in framework, first, coloured image is implemented normalization operation and be red (R), green (G) and blueness (B) three component images by the picture breakdown after normalization; Then, three component images are implemented respectively to Arnold conversion and carry out pixel scramble; Finally, use the Gyrator conversion that Logistic chaotic maps, tent chaotic maps, the anglec of rotation are α, three component images after scramble are combined as to the data message that triple channel structure is relevant; At the second layer, encrypt in framework, first, the relevant data message of this triple channel structure is carried out to Arnold conversion; Then, the result of Arnold conversion is implemented to phase-modulation; Finally, the result of phase-modulation is implemented to Gyrator conversion, complete whole encryption flow, obtain final gray level image information.

2. the single channel color image encrypting method based on GT conversion and chaos as claimed in claim 1, is characterized in that, ground floor is encrypted framework and specifically comprised:

The first step: original color image is carried out to normalization operation, and be decomposed into R, G, tri-component images of B, be expressed as r (x, y), g (x, y) and b (x, y), in every width component image, pixel maximal value is 1;

Second step: it is n that component image r (x, y), g (x, y) and b (x, y) are implemented respectively to iterations ₃, n ₂and n ₁arnold conversion, the noise image after scramble is expressed as A _n3(r (x, y)), A _n2(g (x, y)) and A _n1(b (x, y));

The 3rd step: first obtain first CHAOTIC PHASE MODULATED function, the blue component A of this function after by scramble _n1(b (x, y)) and Logistic Chaotic map sequence C ₁(x, y) combines, and is exp{i π (A _n1(b (x, y))+C ₁(x, y)) }; By the green component A after scramble _n2(g (x, y)) is complex signal H with first CHAOTIC PHASE MODULATED combination of function ₁(x, y), to H ₁(x, y) implements the Gyrator that the anglec of rotation is α and converts the intermediate variable H that obtains green component and blue component _gb(x, y), H _gbthe amplitude of (x, y) is T _gb(x, y), phase place is angle{H _gb(x, y) }; Then calculate second CHAOTIC PHASE MODULATED function, this function is by angle{H _gb(x, y) } and two-dimentional asymmetric tent sequence of mapping C ₂(x, y) forms, and is exp{i π (angle{H _gb(x, y) }+C ₂(x, y)) }; By the red component A after scramble _n3(r (x, y)) is complex signal H with second CHAOTIC PHASE MODULATED combination of function ₂(x, y), to H ₂(x, y) carries out the Gyrator conversion that the anglec of rotation is α, generates the relevant data message H of triple channel _rgb(x, y).

3. the single channel color image encrypting method based on GT conversion and chaos as claimed in claim 1, is characterized in that, second layer encryption framework is specially: the first data message H relevant to triple channel _rgb(x, y) implements iterations is n ₄arnold conversion, result and the chaos sequence exp{i π (C of modulation Arnold conversion ₁(x, y)+C ₂(x, y) }, to exchange the result making and implement α rank Gyrator conversion, the amplitude that extracts transformation results obtains final ciphertext I _final, the phase place of extracting transformation results obtains final phase place P _final.

4. the single channel color image encrypting method based on GT conversion and chaos as claimed in claim 2, is characterized in that, described ground floor is encrypted in the second step of framework, and Arnold is transformed to:

$A_M:\left[\begin{array}{c}{x}^{\&prime;}\\ y^{\&prime;}\end{array}\right]\mathrm{ARP}[f(x,y),M]=\mathrm{mod}\left(\begin{array}{c}\left[\begin{array}{cc}1& 1\\ 1& 2\end{array}\right]\left[\begin{array}{c}x\\ y\end{array}\right],M\end{array}\right)---\left(1\right)$

Formula (1) has defined Arnold conversion, wherein ART represents Arnold conversion, f (x, y) for treating the plaintext image of scramble, f (x, y) size is M * M, (x, y) and (x ', y ') represent respectively Arnold conversion scramble before and the location of pixels after scramble, mod () accords with for complementation.

5. the single channel color image encrypting method based on GT conversion and chaos as claimed in claim 2, is characterized in that, described ground floor is encrypted in the 3rd step of framework, and Gyrator is transformed to:

$f_o(x_o,y_o)=G^{\mathrm{\&alpha;}}\left[f_i(x_i,y_i)\right](x_o,y_o)=\frac{1}{\left|\sin \mathrm{\&alpha;}\right|}\&Integral;\&Integral;f_i(x_i,y_i)K_{\mathrm{\&alpha;}}(x_i,y_i,x_o,y_o){\mathrm{dx}}_i{\mathrm{dy}}_i---\left(2\right)$

Formula (2) has defined optical imagery f _i(x _i, y _i) the result f of α level Gyrator conversion _o(x _o, y _o), K wherein _α(x _i, y _i, x _o, y _o) be the integral kernel function of Gyrator conversion, α is the progression (being the anglec of rotation) of Gyrator conversion, G ^αrepresent α level Gyrator conversion, (x _i, y _i) and (x _o, y _o) represent respectively input, output plane coordinate, ∫ ∫ f _i(x _i, y _i) K _α(x _i, y _i, x _o, y _o) dx _idy _iexpression is to function f _i(x _i, y _i) K _α(x _i, y _i, x _o, y _o) respectively at x _idirection and y _idirection is done integral operation.Sin α is the sine value of progression (being the anglec of rotation) α;

$K_{\mathrm{\&alpha;}}(x_i,y_i,x_o,y_o)=\exp \left(i2\mathrm{\&pi;}\frac{(x_o{y}_o+x_i{y}_i)\cos \mathrm{\&alpha;}-(x_i{y}_o+x_o{y}_i)}{\sin \mathrm{\&alpha;}}\right)---\left(3\right)$

Formula (3) has defined the integral kernel function K of Gyrator conversion _α(x _i, y _i, x _o, y _o), wherein, exp () is exponent arithmetic, and i is the imaginary part of symbol, and π is circular constant, and sin α is the sine value of progression (being the anglec of rotation) α.Cos α is the cosine value of progression (being the anglec of rotation) α.X _ifor input plane x direction coordinate, y _ifor input plane y direction coordinate, x _ofor output plane x direction coordinate, y _ofor output plane y direction coordinate.Hence one can see that, when α=0, and G ⁰{ f _i(x _i, y _i)=f _i(x _i, y _i); It when α=pi/2, is the Fourier transform of coordinate axis rotation pi/2; It when α=π, is inverse Fourier transform; It when the pi/2 of α=3, is the inverse Fourier transform of coordinate axis rotation pi/2.When α is other order, the integral kernel K of Gyrator conversion _α(x _i, y _i, x _o, y _o) there is continuous amplitude and hyperbolic curve phase structure.

6. the single channel color image encrypting method based on GT conversion and chaos as claimed in claim 2, is characterized in that, described ground floor is encrypted in the 3rd step of framework, and Logistic is mapped as:

f(x)＝p·x·(1-x) （4）

Formula (4) has defined 1 dimensional Logistic Map, and wherein fractal parameter p is constant, and 0 < p≤4, and x is independent variable, and f (x) is Logistic mapping value;

x _n+1＝p·x _n·(1-x _n) （5）

Formula (5) is the iteration form of formula (4), and wherein, fractal parameter p is constant, and 0 < p≤4, x _n, x _n+1for chaos sequence value, and x _n∈ (0,1), x _n+1∈ (0,1).

7. the single channel color image encrypting method based on GT conversion and chaos as claimed in claim 2, is characterized in that, described ground floor is encrypted in the 3rd step of framework, and tent is mapped as:

$x_{n+1}=\left\{\begin{array}{c}\frac{x_n}{q}(0\&le;x_n\&le;q)\\ \frac{1-x_n}{1-q}(q\&le;x_n\&le;1)\end{array}\right.---\left(6\right)$

Formula (6) has defined tent mapping, wherein x _n, x _n+1the iteration result that represents the n time and the n+1 time, x ₀for iteration initial value, q is parameter, and when q ∈ (0,1), formula (6) is in chaos state.

8. the single channel color image encrypting method based on GT conversion and chaos as claimed in claim 2, is characterized in that, described ground floor is encrypted in the 3rd step of framework, complex signal H ₁(x, y) is:

H ₁(x,y)＝A _n2(g(x,y))·exp{iπ(A _n1(b(x,y))+C ₁(x,y))} （7）

Formula (7) has defined the green component A after scramble _n2(g (x, y)) and first CHAOTIC PHASE MODULATED function exp{i π (A _n1(b (x, y))+C ₁(x, y)) } the complex signal H that obtains after combination ₁(x, y), wherein exp{} is exponent arithmetic, and i is the imaginary part of symbol, and π is circular constant.

9. the single channel color image encrypting method based on GT conversion and chaos as claimed in claim 2, is characterized in that, described ground floor is encrypted in the 3rd step of framework, complex signal H ₂(x, y) is:

H ₂(x,y)＝A _n3(r(x,y))·exp{iπ(angle{H ₁(x,y)}+C ₂(x,y))} （8）

Formula (8) has defined the red component A after scramble _n3(r (x, y)) and second CHAOTIC PHASE MODULATED function exp{i π (angle{H ₁(x, y) }+C ₂(x, y)) } the complex signal H that obtains after combination ₂(x, y), wherein exp{} is exponent arithmetic, and i is the imaginary part of symbol, and π is circular constant, and angle{} is for extracting phase operation.

10. the single channel color image encrypting method based on GT conversion and chaos as described in claim 1-9 any one, is characterized in that, also comprises decrypting process, described decrypting process is the inverse process of encrypting, comprise two-layer deciphering framework, ground floor deciphering framework is to modulate final ciphertext I _finalwith final phase place P _final, exchange the result enforcement-α rank Gyrator conversion making, the result that modulating transformation obtains and phase place exp{-i π (C ₁(x, y)+C ₂(x, y) }, exchanging the result enforcement iterations making is m ₄contrary Arnold conversion, after conversion, obtain triple channel related data H _rgb(x, y); Second layer deciphering framework is as follows:

The first step: to triple channel related data H _rgb(x, y) enforcement-α rank Gyrator conversion obtains complex signal H ₂(x, y), extracts complex signal H ₂the amplitude of (x, y), it is m that this amplitude is implemented to iterations ₃contrary Arnold conversion obtain red component r (x, y);

Second step: extract complex signal H ₂the phase place of (x, y) obtains angle{H ₂(x, y) }, phase modulation angle{H ₂(x, y) }/π-C ₂(x, y) and amplitude T _gb(x, y), exchanges the result enforcement-α rank Gyrator conversion making and obtains complex signal H ₁(x, y), extracts complex signal H ₁the amplitude of (x, y), it is m that this amplitude is implemented to iterations ₂contrary Arnold conversion obtain green component g (x, y);

The 3rd step: extract complex signal H ₁the phase place of (x, y) obtains angle{H ₁(x, y) }, to phase place angle{H ₁(x, y) }/π-C ₁(x, y) implements iterations is m ₁contrary Arnold conversion obtain blue component b (x, y).Wherein, when plaintext image size is 256 * 256 pixel, m ₁=192-n ₁, m ₂=192-n ₂, m ₃=192-n ₃, m ₄=192-n ₄; When plaintext image size is 512 * 512 pixel, m ₁=384-n ₁, m ₂=384-n ₂, m ₃=384-n ₃, m ₄=384-n ₄.

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